The present invention relates in general to a system and method for generating coefficients for digital filters. The present invention more particularly relates to such a system and method wherein an iterative adaptive process is utilized which employs a least mean square processor with the step size of the filter coefficients in process being related to the stochastic average of the gradients generated during the iterative process.
Digital filters find application in digital circuits, including those implemented in integrated circuit form. Such filters exhibit many advantages such as, for example, high reliability, no drift with time, no drift with temperature, unit-to-unit repeatability, and superior transmission performance. Digital filters can include one or more sections, the number of sections depending mainly upon the desired accuracy in realizing the nominal characteristics of the filter. In other words, an increase in the number of sections a digital filter provides a corresponding increase in the accuracy to which the desired filter characteristics can be obtained.
One application for digital filters is in a subscriber line audio-processing circuit (SLAC). SLAC devices are utilized in telephone systems to perform CODEC and filter functions associated with the two-wire section of the subscriber line circuiting in a digital switch. To that end, these circuits provide conversion of analog voice signals to digital pulse code modulated (PCM) samples for placement of the PCM signals onto a PCM highway, and conversion of digital PCM signals received from the PCM highway into analog voice signals. During this conversion process, digital filters are used to band-limit the voice signals, set gain, perform trans-hybrid balancing, provide adjustment of termination impedance, and provide frequency attenuation adjustment (equalization) of the receive and transmit paths.
To implement a digital filter, it is necessary to provide a filter coefficient for each section or tap of the filter. This is generally accomplished by storing the filter coefficient in a memory of the device employing the filter. The filter coefficient for each filter section is transformed from a single number into a plurality of coefficients known as Canonic Signed Digit (CSD) coefficients before storage into memory. CSD coefficients and the manner in which they may be derived from a single coefficient are well known in the art.
In the prior art, the coefficients for the digital filter section (before conversion into CSD coefficients) were generated by an adaptive iterative least mean square process. During this prior art process, the coefficients of the filter section have been, during each iteration, updated from the last iteration by the instantaneous gradient value. In such a process, the instantaneous gradient, based upon a single sample, is the product of the instantaneous value of a time-varying input signal and the simultaneous instantaneous value of an error signal. The error signal is generated by applying the input signal to both a desired filter characteristic and the filter coefficients in process to generate first and second outputs, and then generating the difference between these output. When the error signal is detected to be below a predetermined standard, the process is stopped and the last set of coefficients used in the process are the final coefficients to be used in the filter after conversion to the CSD format.
While the aforementioned iterative process has been adequate in its use to determine digital filter coefficients, there remains the need for improvement in such processes. More particularly, the prior art least mean square iterative process is not computationally efficient and reasonably fast in convergence unless an optimal step-size is used in a noise-free environment. Unfortunately, it is difficult to find the optimal step-size that satisfies both requirements of fast tracking capability during an adaptive process and small misadjustment error after convergence.
In addition, the foregoing process is sensitive to noise in generating the gradient because the gradient is based upon a single time sample. Hence in practice, the prior art iterative process has required considerable time for completion to arrive at an accurate determination of digital filter coefficients given the fact that it is sensitive to noise and the variable optimum step-size is difficult to determine.
It is therefore a general object of the present invention to provide a new and improved system and method for generating digital filter coefficients.
It is a further object of the present invention to provide such a system and method which is insensitive to noise and wherein the optimum step-size is readily determined.
It is a still further object of the present invention to provide such a system and method wherein the step-size is related to the stochastic average of the gradients generated during the adaptive process.